This thesis investigates the high-order hierarchical finite element method, also known as the finite element p-version, as a computationally-efficient technique for generating numerical solutions to the cardiac monodomain equation. We first present it as a uniform-order method, and through an a priori error bound we explain why the associated cardiac cell model must be thought of as a PDE and approximated to high-order in order to obtain the accuracy that the p-version is capable of. We perform simulations demonstrating that the achieved error agrees very well with the a priori error bound. Further, in terms of solution accuracy for time taken to solve the linear system that arises in the finite element discretisation, it is more efficient that the state-of-the-art piecewise linear finite element method. We show that piecewise linear FEM actually introduces quite significant amounts of error into the numerical approximations, particularly in the direction perpendicular to the cardiac fibres with physiological conductivity values, and that without resorting to extremely fine meshes with elements considerably smaller than 70 micrometres, we can not use it to obtain high-accuracy solutions. In contrast, the p-version can produce extremely high accuracy solutions on meshes with elements around 300 micrometres in diameter with these conductivities. Noting that most of the numerical error is due to under-resolving the wave-front in the transmembrane potential, we also construct an adaptive high-order scheme which controls the error locally in each element by adjusting the finite element polynomial basis degree using an analytically-derived a posteriori error estimation procedure. This naturally tracks the location of the wave-front, concentrating computational effort where it is needed most and increasing computational efficiency. The scheme can be controlled by a user-defined error tolerance parameter, which sets the target error within each element as a proportion of the local magnitude of the solution as measured in the H^1 norm. This numerical scheme is tested on a variety of problems in one, two and three dimensions, and is shown to provide excellent error control properties and to be likely capable of boosting efficiency in cardiac simulation by an order of magnitude. The thesis amounts to a proof-of-concept of the increased efficiency in solving the linear system using adaptive high-order finite elements when performing single-thread cardiac simulation, and indicates that the performance of the method should be investigated in parallel, where it can also be expected to provide considerable improvement. In general, the selection of a suitable preconditioner is key to ensuring efficiency; we make use of a variety of different possibilities, including one which can be expected to scale very well in parallel, meaning that this is an excellent candidate method for increasing the efficiency of cardiac simulation using high-performance computing facilities.

L'objet de cette thèse est l'analyse multifractale des fonctions autosimilaires et l'étude de la validité du formalisme multifractal. Il s'agit d'abord de déterminer la régularité Hölderienne ponctuelle exacte pour des fonctions dont le graphe localement est grossièrement une contraction du graphe complet, à une fonction erreur près ; ensuite de calculer les dimensions de Hausdorff des ensembles de points où la fonction présente la même singularité; et enfin de vérifier les conjectures de Frish et Parisi et celle d'Arneodo, Bacry et Muzy, qui relient ces dimensions à des quantités moyennes extraites de la fonction. Nous étudions plusieurs types d'autosimilarités, et montrons (en reformulant parfois) que l'analyse par ondelettes permet d'étudier la validité de ces relations.

Includes supplemental material. / Disaster relief operations, such as the 2005 Tsunami and Hurricane Katrina, and wartime operations, such as Operation Enduring Freedom and Operation Iraqi Freedom, have identified the need for a standardized command and control system interoperable among Joint, Coalition, and Interagency entities. The Systems Engineering Analysis Cohort 9 (SEA-9) Rapid Response Command and Control (R2C2) integrated project team completed a systems engineering (SE) process to address the military’s command and control capability gap. During the process, the R2C2 team conducted mission analysis, generated requirements, developed and modeled architectures, and analyzed and compared current operational systems versus the team’s R2C2 system. The R2C2 system provided a reachback capability to the Regional Combatant Commander’s (RCC) headquarters, a local communications network for situational assessments, and Internet access for civilian counterparts participating in Humanitarian Assistance/Disaster Relief operations. Because the team designed the R2C2 system to be modular, analysis concluded that the R2C2 system was the preferred method to provide the RCC with the required flexibility and scalability to deliver a rapidly deployable command and control capability to perform the range of military operations.

The thesis concerns the mathematical study of the calculus of variations and its application to liquid crystals. In the first chapter we examine vectorial problems in the calculus of variations with an additional pointwise constraint so that any admissible function <strong>n</strong> ε W^1,1(ΩM), and M is a manifold of suitable regularity. We formulate necessary and sufficient conditions for any given state <strong>n</strong> to be a strong or weak local minimiser of I. This is achieved using a nearest point projection mapping in order to use the more classical results which apply in the absence of a constraint. In the subsequent chapters we study various static continuum theories of liquid crystals. More specifically we look to explain a particular cholesteric fingerprint pattern observed by HP Labs. We begin in Chapter 2 by focusing on a specific cholesteric liquid crystal problem using the theory originally derived by Oseen and Frank. We find the global minimisers for general elastic constants amongst admissible functions which only depend on a single variable. Using the one-constant approximation for the Oseen-Frank free energy, we then show that these states are global minimisers of the three-dimensional problem if the pitch of the cholesteric liquid crystal is sufficiently long. Chapter 3 concerns the application of the results from the first chapter to the situations investigated in the second. The local stability of the one-dimensional states are quantified, analytically and numerically, and in doing so we unearth potential shortcomings of the classical Oseen-Frank theory. In Chapter 4, we ascertain some equivalence results between the continuum theories of Oseen and Frank, Ericksen, and Landau and de Gennes. We do so by proving lifting results, building on the work of Ball and Zarnescu, which relate the regularity of line and vector fields. The results prove to be interesting as they show that for a director theory to respect the head to tail symmetry of the liquid crystal molecules, the appropriate function space for the director field is S BV² (Ω,S<sup>2,/sup>). We take this idea and in the final chapter we propose a mathematical model of liquid crystals based upon the Oseen-Frank free energy but using special functions of bounded variation. We establish the existence of a minimiser, forms of the Euler-Lagrange equation, and find solutions of the Euler-Lagrange equation in some simple cases. Finally we use our proposed model to re-examine the same problems from Chapter 2. By doing so we extend the analysis we were able to achieve using Sobolev spaces and predict the existence of multi-dimensional minimisers consistent with the known experimental properties of high-chirality cholesteric liquid crystals.

Le syndrome de Lynch est une affection héréditaire autosomique dominante due à des mutations constitutionnelles des gènes du système de réparation de l'ADN (MLH1, MSH2 et MSH6). Depuis 20 ans le réseau français des laboratoires impliqués dans le syndrome de Lynch a identifié un total de 6687 variants. Sept cent sept d'entre eux, essentiellement des variants faux sens, restent encore des variants de signification inconnue (VSI), sans utilité pour le conseil génétique. Le but de notre étude était de développer un algorithme permettant de classer les variants de signification inconnue. Les critères utilisés étaient les données des analyses in silico, phénotypiques (ségrégation, critères d'Amsterdam), l'état de la fonction MMR (MisMatch Repair) dans les cellules tumorales, les tests fonctionnels et d'épissage, ainsi que les données publiées. Cet algorithme a été appliqué à l'ensemble des VSI de la base de données française et nous a permis de caractériser 370 variants . Les données ont été intégrées dans la base de données française UMD des gènes MMR afin d'être disponibles pour la communauté scientifique. Grace aux données collectées par le réseau, nous avons également pu caractériser le phénotype du syndrome de Lynch. Nous avons ainsi confirmé que le cancer du sein ne fait pas partie du spectre du syndrome de Lynch et que les formes de ce syndrome associées à une mutation du gène EPCAM n'entrainent qu'un risque très faible de cancers de l'endomètre, permettant ainsi d'adapter les recommandations de suivi dans cette situation.de l'endomètre, permettant ainsi d'adapter les recommandations de suivi dans cette situation. / Lynch syndrome is a frequent cancer predisposition with an autosomal dominant mode of inheritance and caused by heterozygous germ line mutations in one of the major DNA mismatch repair (MMR) genes (MLH1, MSH2 and MSH6). For 20 years, the French laboratories network involved in Lynch syndrome identified a total of 6687 variations. Among them, 707, mainly missense variations, remained variants of uncertain significance (VUS), thus could not be used for reliable genetic counseling. The aim of our study was to develop an algorithm able to classify VUS, according to the international consensus (IARC). This algorithm was constructed based on criteria usually required for genetic characterization such as in silico analysis, phenotypical data (segregation, Amsterdam criteria's), MMR status in tumor cells, functional assays, splicing analyses and published data. Data were registered in the French database. As a result of this work, we were able to classify 370 variants of the 707 (52,3%). As part of this work, we also analyzed phenotypical data of patients with Lynch syndrome and showed that breast cancer can definitively be excluded from the spectrum of Lynch-related cancers, and that EPCAM mutations, which may lead to Lynch syndrome, are associated with a very low incidence of endometrial cancer and have probably to be considered as an allelic disease with specific clinical recommendations.

The goal of Master's Thesis is an identification of life cycle costs of vacuum cleaners. Next point is an analysis of these life cycle cost by using value analysis. The theoretical part is focused on definitions of Life Cycle Costing (LCC) and Value Analysis (VA). The practical part, which is fundamental, contains identification of life cycle cost of selected vacuum cleaners, life cycle costing of selected vacuum cleaners and their value analysis. Result of this Master's Thesis is an interpretation of the results and the suggestion of steps for consumers and producers of vacuum cleaners.

[pt] Berger e Podolak apresentaram uma interpretação geométrica do resultado seminal de Ambrosetti e Prodi sobre o comportamento das soluções de certas equações diferenciais parciais elípticas semi-lineares. Consideram-se extensões deste ponto de vista, a partir das quais se desenvolve um algoritmo numérico para resolver as equações. / [en] Berger and Podolak obtained a geometric interpretation of the seminal result of Ambrosetti and Prodi regarding the behavior of solutions of certain semilinear elliptic partial differential equations. We consider extensions of such interpretation to develop a stable numerical algorithm that solves the equations.

Les grandes matrices de covariance constituent certainement l’un des modèles les plus utiles pour les applications en statistiques en grande dimension, en communication numérique, en biologie mathématique, en finance, etc. Les travaux de Marcenko et Pastur (1967) ont permis de décrire le comportement asymptotique de la mesure spectrale de telles matrices formées à partir de N copies indépendantes de n observations d’une suite de variables aléatoires iid et sa convergence vers une distribution de probabilité déterministe lorsque N et n convergent vers l’infini à la même vitesse. Plus récemment, Merlevède et Peligrad (2016) ont démontré que dans le cas de grandes matrices de covariance issues de copies indépendantes d’observations d’un processus strictement stationnaire centré, de carré intégrable et satisfaisant des conditions faibles de régularité, presque sûrement, la distribution spectrale empirique convergeait étroitement vers une distribution non aléatoire ne dépendant que de la densité spectrale du processus sous-jacent. En particulier, si la densité spectrale est continue et bornée (ce qui est le cas des processus linéaires dont les coefficients sont absolument sommables), alors la distribution spectrale limite a un support compact. Par contre si le processus stationnaire exhibe de la longue mémoire (en particulier si les covariances ne sont pas absolument sommables), le support de la loi limite n'est plus compact et des études plus fines du comportement des valeurs propres sont alors nécessaires. Ainsi, cette thèse porte essentiellement sur l’étude des asymptotiques et des fluctuations des plus grandes valeurs propres de grandes matrices de covariance associées à des processus stationnaires à longue mémoire. Dans le cas où le processus stationnaire sous-jacent est Gaussien, l’étude peut être simplifiée via un modèle linéaire dont la matrice de covariance de population sous-jacente est une matrice de Toeplitz hermitienne. On montrera ainsi que dans le cas de processus stationnaires gaussiens à longue mémoire, les fluctuations des plus grandes valeurs propres de la grande matrice de covariance empirique convenablement renormalisées sont gaussiennes. Ce comportement indique une différence significative par rapport aux grandes matrices de covariance empirique issues de processus à courte mémoire, pour lesquelles les fluctuations de la plus grande valeur propre convenablement renormalisée suivent asymptotiquement la loi de Tracy-Widom. Pour démontrer notre résultat de fluctuations gaussiennes, en plus des techniques usuelles de matrices aléatoires, une étude fine du comportement des valeurs propres et vecteurs propres de la matrice de Toeplitz sous-jacente est nécessaire. On montre en particulier que dans le cas de la longue mémoire, les m plus grandes valeurs propres de la matrice de Toeplitz convergent vers l’infini et satisfont une propriété de type « trou spectral multiple ». Par ailleurs, on démontre une propriété de délocalisation de leurs vecteurs propres associés. Dans cette thèse, on s’intéresse également à l’universalité de nos résultats dans le cas du modèle simplifié ainsi qu’au cas de grandes matrices de covariance lorsque les matrices de Toeplitz sont remplacées par des matrices diagonales par blocs / Large covariance matrices play a fundamental role in the multivariate analysis and high-dimensional statistics. Since the pioneer’s works of Marcenko and Pastur (1967), the asymptotic behavior of the spectral measure of such matrices associated with N independent copies of n observations of a sequence of iid random variables is known: almost surely, it converges in distribution to a deterministic law when N and n tend to infinity at the same rate. More recently, Merlevède and Peligrad (2016) have proved that in the case of large covariance matrices associated with independent copies of observations of a strictly stationary centered process which is square integrable and satisfies some weak regularity assumptions, almost surely, the empirical spectral distribution converges weakly to a nonrandom distribution depending only on the spectral density of the underlying process. In particular, if the spectral density is continuous and bounded (which is the case for linear processes with absolutely summable coefficients), the limiting spectral distribution has a compact support. However, if the underlying stationary process exhibits long memory, the support of the limiting distribution is not compact anymore and studying the limiting behavior of the eigenvalues and eigenvectors of the associated large covariance matrices can give more information on the underlying process. This thesis is in this direction and aims at studying the asymptotics and the fluctuations of the largest eigenvalues of large covariance matrices associated with stationary processes exhibiting long memory. In the case where the underlying stationary process is Gaussian, the study can be simplified by a linear model whose underlying population covariance matrix is a Hermitian Toeplitz matrix. In the case of stationary Gaussian processes exhibiting long memory, we then show that the fluctuations of the largest eigenvalues suitably renormalized are Gaussian. This limiting behavior shows a difference compared to the one when large covariance matrices associated with short memory processes are considered. Indeed in this last case, the fluctuations of the largest eigenvalues suitably renormalized follow asymptotically the Tracy-Widom law. To prove our results on Gaussian fluctuations, additionally to usual techniques developed in random matrices analysis, a deep study of the eigenvalues and eigenvectors behavior of the underlying Toeplitz matrix is necessary. In particular, we show that in the case of long memory, the largest eigenvalues of the Toeplitz matrix converge to infinity and satisfy a property of “multiple spectral gaps”. Moreover, we prove a delocalization property of their associated eigenvectors. In this thesis, we are also interested in the universality of our results in the case of the simplified model and also in the case of large covariance matrices when the Toeplitz matrices are replaced by bloc diagonal matrices

De nos jours, les progrès de l’informatisation de l’imagerie médicale assistent au plus près les médecins dans leur soin au patient. Des modèles personnalisés computationnels sont utilisés pour le diagnostique, prognostique et planification du traitement, en diminuant lesrisques pour le patient, et potentiellement les frais médicaux.Heartflow est l’exemple même d’une compagnie qui réussit ce service dans le domaine cardiovasculaire. À partir d’un modèle extrait d’images tomographiques rayons X, les lésions avec impact fonctionnel sont identifiées dans les artères coronaires. Cette analyse qui combine l’anatomie à la fonction est néanmoins limitée par la résolution de l’image. En aval de ces larges vaisseaux, un examen fonctionnel dénommé Imagerie de Perfusion du Myocarde (IPM) met en évidence les régions du myocarde affectées par un déficit de flux sanguin. Cependant, l’IPM n’établie pas de relation fonctionnelle avec les larges vaisseaux coronaires lésés en amont.L’objectif de ce projet est de construire la connexion fonctionnelle entre les coronaires et le myocarde, en extrapolant l’analyse fonctionnelle depuis les larges vaisseaux vers le lit capillaire. À cette fin, il faut étendre le modèle vasculaire jusqu'aux microvaisseaux, et mener une analyse fonctionnelle en direction du comportement myocardique.Nous étendons une méthode de génération d’arbre vasculaire basée sur la satisfaction de principes fonctionnels, nommée Constrained Constructive Optimization (Optimization Constructive sous Contraintes), pour qu’elle s’applique à de multiples arbres vasculaires en compétition. L’algorithme simule l’angiogénèse avec minimisation du volume vasculaire sous contraintes de flux et de géométrie adaptant la croissance simultanée des arbres aux caractéristiques du patient. Cette méthode fournit un modèle hybride composé de coronaires épicardiales extraites d’images et de vaisseaux synthétiques jusqu’aux artérioles, emplissant le ventricule gauche du myocarde.Puis, nous construisons un pipeline d’analyse fonctionnelle multi-échelle pour étendre la simulation de flux depuis les coronaires vers le myocarde. Cela consiste en un modèle de flux coronaire 1D compatible avec la vasculature hybride, et l’analyse de la distribution spatiale des flux provenant des segments terminaux. Cette dernière est réalisée dans une nomenclature similaire à celle de l’IPM pour permettre la comparaison avec des données de vérité terrain fonctionnelles.Nous avons relié l’anatomie du réseau vasculaire à la distribution de flux dans le myocarde pour plusieurs patients. Cette analyse multi-échelle permet d’identifier des pistes pour affiner les méthodes de génération vasculaire et de simulation de flux. Cette extrapolation anatomique et fonctionnelle personnalisée est une première passerelle pour la simulation de perfusion du myocarde à partir d’imagerie tomographique scanner. La construction d’un tel modèle computationnel personnalisé pourrait aider à la compréhension de la physio-pathologie cardiovasculaire complexe et, enfin, à la santé du patient. / Recent advances in medical image computing have allowed automatedsystems to closely assist physicians in patient therapy. Computationaland personalized patient models benefit diagnosis, prognosisand treatment planning, with a decreased risk for the patient,as well as potentially lower cost. HeartFlow Inc. is a successfull exampleof a company providing such a service in the cardiovascularcontext. Based on patient-specific vascular model extracted from XrayCT images, they identify functionally significant disease in largecoronary arteries. Their combined anatomical and functional analysisis nonetheless limited by the image resolution. At the downstreamscale, a functional exam called Myocardium Perfusion Imaging (MPI)highlights myocardium regions with blood flow deficit. However,MPI does not functionally relate perfusion to the upstream coronarydisease.The goal of our project is to build the functional bridge betweencoronary and myocardium, by extrapolating the functional analysisfrom large coronary toward the capillary bed. This objective requiresextension from the coronary model down to the microvasculaturecombined with a functional analysis leading to the myocardium compartment.We expand a tree generation method subjected to functional principles,named Constrained Constructive Optimization, to generate multiplecompeting vascular trees. The algorithm simulates angiogenesisunder vascular volume minimization with flow-related and geometricalconstraints, adapting the simultaneous tree growths to patientpriors. This method provides a hybrid image-based and synthetic geometricmodel, starting from segmented epicardium coronary downto synthetic arterioles, filling the left ventricle myocardium.We then build a multiscale functional analysis pipeline to allowblood flow simulation from the coronaries to the myocardium. Thisis achieved with a 1D coronary model compatible with the hybridvasculature, and a spatial blood flow distribution analysis of the terminalsegments. The latter is performed using a similar nomenclatureto MPI, to enable patient-specific comparison with functional groundtruthdata.We connected the vascular anatomy to blood flow distribution inthe myocardium on several patient datasets. This multiscale frameworkpoints out several leads to refine the vascular network generationand fluid simulation methods. This patient-specific anatomicaland functional extrapolation is a first gateway toward myocardiumperfusion from X-ray CT data. Building such personalized computational model of patient could potentially help investigating cardiovascularcomplex physio-pathology, and, finally, improve the patientcare.

Molibdênio é um elemento traço envolvido na fixação de nitrogênio, enxofre e carbono. Oligopeptídeos estão envolvidos na nutrição bacteriana e diversos outros processos de sinalização intercelular. O objetivo do presente estudo foi investigar o papel funcional das proteínas ligadoras dos sistemas de captação de molibdato (ModA) e oligopeptídeo (OppA) em Xanthomonas axonopodis pv. citri em condições in vitro e in vivo. O mutante ModA mostrou uma produção diminuída de goma xantana, alteração do biofilme e adesão prejudicada em condições in vitro. In vivo a interação do mutante modA mostrou alterações nas lesões causadas em folhas de grapefruit possivelmente resultado da baixa expressão do gene gumB. O mutante na proteína OppA apresentou células mais co-agregadas alterando a estrutura do biofilme e consequentemente diminuindo sua capacidade de adesão. In vivo, a linhagem mutante não alterou o fenótipo de patogenicidade, mas a sua capacidade de crescimento foi afetada no início da fase estacionária sugerindo que o sistema Opp desempenha um papel nutricional. / Molybdenum is a trace element involved in nitrogen fixation, sulfur and carbon. Oligopeptides are involved in bacterial nutrition and several other intercellular signaling processes. The aim of this study was to investigate the functional role of binding proteins of molybdate (ModA) and oligopeptide (OppA) uptake systems of Xanthomonas campestris pv. citri in in vitro and in vivo conditions. ModA mutant showed a decreased production of xanthan gum, altered biofilm and adhesion impaired in vitro conditions. In vivo ModA mutant interaction showed changes in injuries on leaves of grapefruit possibly due to low expression of the gumB gene. The OppA mutant showed more cells co-aggregated by changing the structure of the biofilm and consequently reducing their capacity to adhere. In vivo, the mutant strain did not modify the phenotype of pathogenicity, but its ability for growth was affected at the early stationary phase suggesting that the Opp system plays a nutritional role.